Astronomers studying a distant planetary system detect a uniform cosmic relic background radiation. The total intensity of this background radiation is 8.5×10−6 W m−28.5 \times 10^{-6}\text{ W m}^{-2}8.5×10−6 W m−2 and its spectrum exhibits a peak intensity at a wavelength of 0.82 mm0.82\text{ mm}0.82 mm.
Calculate the energy of a single photon at this peak wavelength.
Estimate the number of such photons incident per second on a detector test surface with an area of 120 cm2120\text{ cm}^2120 cm2. Assume all incident photons have this peak wavelength.
A researcher proposes using large shallow water collectors to absorb this radiation for heating. Estimate the maximum rise in temperature per second of a cylindrical volume of water with a depth of 3.5 m3.5\text{ m}3.5 m, assuming all radiation incident on the flat top of the volume is fully absorbed. (Density of water =1000 kg m−3= 1000\text{ kg m}^{-3}=1000 kg m−3, specific heat capacity of water =4200 J kg−1 K−1= 4200\text{ J kg}^{-1}\text{ K}^{-1}=4200 J kg−1 K−1)
